Optimization and Computational Fluid Dynamics - Department of ...

7 CFD-based Optimization for Automotive Aerodynamics 209
Best Cd
0.126
0.124
0.122
0.120
0.118
0.116
AGA GA
(α; β; γ)=(18.7; 19.1; 9.0)
0.114
(α; β; γ)=(18.7; 19.1; 9.1)
0.112
0 50 100 150 200
Number of evaluations
Fig. 7.10 Convergence history
putation is performed until a stationary state is observed for the main aerodynamic
coefficients. This requires approximately 14 hours computational
(CPU) time on a single-processor machine. In order to achieve a reasonable
computational time, parallel evaluations on a cluster of workstations have
been done.
(iii) Optimization method
Two different global optimization methods have been compared on this problem.
The first one is a classical GA with a population number Np equal to
20, a crossover and a mutation coefficient equaling to 0.9 and0.6, respectively.
The second method is similar to GA but with fast and approximated
evaluations as presented in Sect. 7.3.3 (AGA). Note that the hybrid methods
introduced in Sect. 7.3.2 have also been tested on this problem but are
not presented here since AGA performs better. In contrast to these three
global optimization methods, it is worth mentioning that a pure deterministic
method like BFGS fails to find the global drag minimum at all (see [5] for
a further comparison of all these methods).
7.4.3 Numerical Results
The convergence history of both optimization methods GA and AGA for the
present drag reduction problem is depicted in Fig. 7.10. This figure shows
in particular that both methods have nearly reached the same drag value,